Adjointness in Foundations
Article
Formal Antecedent
Category Theory
Citation
F. William Lawvere. (1969). Adjointness in Foundations. Dialectica. 23. pp. 281–296.
Why this reference is included
Lawvere’s 1969 Adjointness in Foundations, published in Dialectica, is one of the program’s working technical references. Cited across Book VII (Categorical Metaphysics), Part 1, Chapter Archetypes as Minimal j-Closed Fixed Points; Book VII (Categorical Metaphysics), Part 7, Chapter Dignity as Meta-Ethical Foundation — the central framing is “The operator j : Ω Ω satisfies the Lawvere–Tierney axioms : (LT1): j ∘ true = true (truth is closed)”.
Cited in
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Book VII — Categorical Metaphysics Part 1Chapter Archetypes as Minimal j-Closed Fixed Points
The operator j : Ω Ω satisfies the Lawvere–Tierney axioms : (LT1): j ∘ true = true (truth is closed)
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Book VII — Categorical Metaphysics Part 7Chapter Dignity as Meta-Ethical Foundation
(i)–(iii): By standard results on reflective subcategories and Lawvere–Tierney topologies (Mac Lane and Moerdijk, Sheaves in Geometry and Logic)